The importance of sustained compliance with physical distancing during COVID-19 vaccination rollout

Background Increasing vaccination coverage against SARS-CoV-2 enabled relaxation of lockdowns in many countries in Europe. As the vaccination rollouts progressed, the public health authorities were seeking recommendations on the continuation of physical distancing measures during ongoing vaccination rollouts. Compliance with these measures was declining while more transmissible virus variants have emerged. Methods We used a SARS-CoV-2 transmission model to investigate the feedback between compliance, infection incidence, and vaccination coverage. We quantified our findings in terms of cumulative number of new hospitalisations three and six months after the start of vaccination. Results Our results suggest that the combination of fast waning compliance in non-vaccinated individuals, low compliance in vaccinated individuals, low vaccine efficacy against infection and more transmissible virus variants may result in a higher cumulative number of new hospitalisations than in a situation without vaccination. These adverse effects can be alleviated by deploying behavioural interventions that should preferably target both vaccinated and non-vaccinated individuals. The choice of the most appropriate intervention depends on vaccination rate and vaccine efficacy against infection. Conclusions Supplementary behavioural interventions aiming to boost compliance to physical distancing measures can improve the outcome of vaccination programmes, until vaccination coverage is sufficiently high. For optimal results, these interventions should be selected based on the vaccine efficacy against infection and expected vaccination rate. While we considered the dynamics of SARS-CoV-2, the qualitative effects of the interplay between infectious disease spread and behavior on the outcomes of a vaccination programme can be used as guidance in a future similar pandemic.


Infection transmission rates matrix 13
In this section we derive details of the transmission rate matrix M given by equation (1) in the main text. In the 14 interest of convenience, we give it here with the meaning of its entries: r 1 r 2 r 1 r 2 1 r 1 r 2 r 2 r 1 r 2 r 2 with where [M ] 11 captures the transmission of infection from non-compliant I to non-compliant S, [M ] 12 from compliant ble individuals S C by infectious individuals who are vaccinated I V . We are assuming frequency dependent mixing.
transmission per contact ( ) and probability that the infectious individual is vaccinated infectious individual. This 23 latter probability at time t is given by 24 cr 2 cN (t) + cr 1 N C (t) + cr 2 N V (t) Constants c in the numerator and denominator cancel out, and therefore the rate with which susceptible individuals 25 S C get infected by vaccinated infectious individuals I V at time t is given by Other entries of matrix M given by equation (1) in the main text and by equation (1) in Supplementary materials 27 can be derived using a similar procedure.

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For all strains, the qualitative dynamics observed when vaccination rollout is not accompanied by additional in-38 terventions is similar (Supplementary Figures 2a, 2b, 3a, 3b, 4a, and 4b). More specifically, there is a region for 39 vaccine efficacy and vaccination uptake rate, where the cumulative number of infections exceeds the number for the 40 no-vaccination scenario three and six months after the start of the vaccination rollout. The highest increase above 41 the numbers seen for the no-vaccination scenario is expected for a high uptake rate and low vaccine efficacy. Gen-42 erally speaking, if the vaccination campaign is not accompanied by compliance-targeting interventions, to achieve a 43 better result than the no-vaccination scenario, the vaccine efficacy should exceed a certain threshold. This threshold 44 decreases with increasing vaccination uptake rate.

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For all three strains the threshold vaccine efficacy is lower six months after the start of the vaccination rollout than 46 it is after three. However, for the more infectious strains, the difference in the threshold vaccine efficacy is smaller  Vaccination rollout not supplemented with compliance interventions three and six months into the vaccination rollout, respectively. c and d Vaccination rollout supplemented with compliance interventions targeting non-vaccinated individuals three and six months into the vaccination rollout, respectively. e and f Vaccination rollout supplemented with compliance interventions targeting vaccinated individuals three and six months into the vaccination rollout, respectively. g and h Vaccination rollout supplemented with compliance interventions targeting both vaccinated and non-vaccinated individuals three and six months into the vaccination rollout, respectively. Magenta curves mark boundaries between parameter regions with different sign of the cumulative number of new infections. The scale of x-axes is not linear since vaccination coverage depends non-linearly on the vaccine uptake rate.
Additional physical distancing intervention during the vaccination roll-74 out 75 We considered a scenario where if during the vaccination rollout the prevalence of new infectious cases exceeds 76 a certain threshold, the lockdown that we assumed was in place during the vaccination rollout becomes stricter, a and b Vaccination rollout not supplemented with compliance interventions three and six months into the vaccination rollout, respectively. c and d Vaccination rollout supplemented with compliance interventions targeting non-vaccinated individuals three and six months into the vaccination rollout, respectively. e and f Vaccination rollout supplemented with compliance interventions targeting vaccinated individuals three and six months into the vaccination rollout, respectively. g and h Vaccination rollout supplemented with compliance interventions targeting both vaccinated and non-vaccinated individuals three and six months into the vaccination rollout, respectively. Magenta curves mark boundaries between parameter regions with different sign of the cumulative number of new infections. The scale of x-axes is not linear since vaccination coverage depends non-linearly on the vaccine uptake rate.
further diminishing the average contact rate. Once the prevalence falls bellow the threshold, the lockdown is being 78 relaxed to its prior state. We refer to this intervention "dynamic" lockdown. We investigated the sensitivity of the Vaccination rollout not supplemented with compliance interventions three and six months into the vaccination rollout, respectively. c and d Vaccination rollout supplemented with compliance interventions targeting non-vaccinated individuals three and six months into the vaccination rollout, respectively. e and f Vaccination rollout supplemented with compliance interventions targeting vaccinated individuals three and six months into the vaccination rollout, respectively. g and h Vaccination rollout supplemented with compliance interventions targeting both vaccinated and non-vaccinated individuals three and six months into the vaccination rollout, respectively. Magenta curves mark boundaries between parameter regions with different sign of the cumulative number of new infections. The scale of x-axes is not linear since vaccination coverage depends non-linearly on the vaccine uptake rate.
The model parameters and initial conditions were fixed to the values used in the main text.

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To perform the simulations we fixed the initial conditions and parameters to the values used in the main analyses.

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We assume that the lockdown reduces the average contact rate from 5 to 3 individuals per day. This is comparable the no-vaccination scenario is sensitive to the lockdown threshold value after six months of the vaccination rollout.

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In contrast, at three months after the vaccination rollout the threshold does not affects outcomes. After six months 93 of the vaccination rollout, we observe that as the threshold for initiation (and relaxation) of the lockdown increases, 94 the cumulative number of new infections increases as well. However, when the vaccination rollout is supplemented 95 with "dynamic" lockdown, the cumulative number of new infections is expected to decrease below the level of 96 no-vaccination. It will decrease more for a fast vaccination rate than for a slow vaccination rate.

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We also investigated the improvements achieved by supplementing the vaccination rollout with a "dynamic" lock-98 down ( Supplementary Figures 8-9). We observe that the "dynamic" lockdown can lower the cumulative number 99 of new infections almost two fold in the short term (three months after the start of the vaccination rollout) and 100 more than that in the long term (six months after the start of the vaccination rollout) as compared with no- In the main analysis, we calibrated the percentage of the population compliant with physical distancing measures 121 at the start of the vaccination rollout using reported compliance of 65% with a specific measure (keeping 1.5m 122 distance) in the Netherlands on the week of November 11-17, 2020 [2] . We used this number as a proxy to being 123 compliant to recommended physical distancing measures, and subsequently substantially reducing contact rates.

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In what follows, we vary the initial percentage in a range of 20 − 90% for the percentage of the population that  Figure 10b).

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The model predicts that the excess of infections reported in the main analysis is preserved for the range of percentages 133 of compliant individuals that we considered ( Supplementary Figures 10c and 10d). This percentage is an increases

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We defined seroprevalence as the proportion of the population that has been infected with SARS-CoV-2 and is 140 immune to a new infection at the start of the simulations. In the main analysis we calibrated the model to a 141 seroprevalence of 8%, which is between what was measured in the Netherlands in September/October 2020 [3] and 142 in February 2021 [4] . We explored the sensitivity of the outputs to the initial value of seroprevalence, by varying 143 the initial seroprevalence in the range of 5-20% (Supplementary Figure 11). We kept the sizes of the exposed and The model predicts that the cumulative number of new infections is lower for higher seroprevalence. This is observed 147 in the short term (three months following the vaccination rollout, Supplementary Figure 11a) and in the long term 148 (six months following the vaccination rollout, Supplementary Figure 11b).

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Our simulations show that the excess infections seen in the main analysis is preserved for a wide range of seropreva-150 lence values ( Supplementary Figures 11c and 11d). For a fast vaccination rate the relative excess is much larger  Figures 12c and 12d). For slow vaccination rollout, the excess is 168 decreasing with increasing number of infectious individuals, both in the long term and in the short term. In 169 contrast, for a fast vaccination rate, for a low initial initial number of infectious individuals, the excess increases, 170 while for a higher number it decreases. This relationship is present both in the short term (three months after the 171 start of the vaccination rollout) and in the long term (six months after the start of the vaccination rollout). We 172 note that changes in the relative excess of infections in the range of the number of infectious individuals that we 173 considered does not exceed 3%, thus indicating a low sensitivity of the outputs to variations in this initial condition.
174 Proportion of exposed cases

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In the main analysis we set number of infectious of exposed individuals to be equal to 64249 individuals (0.38% of 176 the population size of the Netherlands) which we calculate using the approximation to the total number of infectious 177 cases made by RIVM for the week November 11-1. We explored the impact of the initial proportion of exposed cases 178 on epidemic and compliance dynamics by sampling the prevalence in the range of 0.1-1% of the total population 179 (Supplementary Figures 12). As the size of the exposed compartment changed, we kept the size of the infectious 180 and recovered compartments fixed to the values used in the main analysis. To preserve the constant size of the 181 total population, we adjusted the size of the susceptible compartment.

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The model predicts that the cumulative number of new infections increases as the proportion of exposed cases 183 at the start of the vaccination rollout increases. This is observed in the short term (three months following the Our simulations indicate that the excess of the new infections as compared to the baseline no-vaccination scenario is 187 preserved for all the values of percentage of exposed individuals that we have sampled. We also observe a relatively 188 low sensitivity of the relative excess of new infections to changes in the initial percentage of exposed individuals 189 ( Supplementary Figures 13c and 13d) when the vaccination uptake is low. In this case, the relative excess of the 190 cumulative number of infections remains on approximately the same level on the whole range that we considered. On 191 the other hand, given the fast vaccination rate, we observe that the relative excess increases as the initial proportion 192 of exposed individuals increases and that the outputs corresponding to endpoints of the exposed percentage interval 193 are approximately 5% apart, both for three and six months. In this section we consider the sensitivity of the outputs to the selected values of the average duration of the exposed 207 period (1/α) and the average duration of the infectious period (1/γ). In the main text they are fixed to be 4 and 7 208 days, respectively. Here we sample 1/α in the range of 2-6 days and 1/γ in the range of 5-9 days (Supplementary 209 Figure 14).

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We observe that the epidemic burden increases as the infectious period increases, such that when the vaccination 211 rate is fast the increase in the cumulative number of new infections is higher than when the vaccination rate is slow.

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On the other hand, we observe that when the length of the exposed period has very little bearing on the cumulative Our results indicate the relative excess of infections as compared to the no-vaccination scenario is preserved through-215 out the ranges that we have considered (Supplementary Figure 15). However, the sensitivity of the magnitude of the 216 excess to variation in the average duration of exposed and infectious periods depend on the vaccination uptake rate.

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If the vaccination rate is slow, than the largest change in the excess that we have measured across the parameter 218 range was approximately equal to 13%. For the vast vaccination rate, especially at a later time the expected excess 219 ranged from almost 14% to 99%. The excess in the cumulative number of infections is increasing as either the 220 average duration of the infectious period and of the average duration of the exposed period increases. However, the 221 changes are more drastic for the former than for the latter. Compliance acquisition and loss rates 239 We considered the sensitivity of the outputs to the rate of moving to the compliant state (δ), and to the average 240 duration of compliant state when there is no vaccination (1/mu 0 ). In the main text we set the compliance duration 241 when there is no vaccination to 30 days. This is an assumed value and here we test the effect of shorter duration 242 of compliance on epidemic dynamics. We consider a range of compliance duration between 7 and 30 days. In the 243 main text we fixed the rate of moving to the compliant state to 4 × 10 −5 per day. Here, we considered the range of